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Analysis of soil nitrogen mineralization as estimated by exponential models
0038-0717,90 53.00+ 0.00 Copyright C 1990 Pergamoa Press pk
Sod Bid. Biochem. Vol. 22, No. 8. pp. 1151-1153, 1990 Printedin Great Britain.All rights-cd
ANALYSIS OF SOIL NITROGEN MINERALIZATION ESTIMATED BY EXPONENTIAL MODELS
AS
JORGESIERRA* Departamento
Suelos, Facultad de Agronomia
UBA,
(Accepted
Av. San Martin
4453.1417
Buenos Aires. Argentina
5 June 1990)
Summary-The simple and the double exponential models used to describe the soil N mineralization process were analyzed by using a central finite differences approximation. Various investigators have found that these models show deficiencies in estimating the mineralization N pools. This paper investigates the possible causes of such deficiencies. The mineralization rate was observed to decrease continuously as the N mineralization proceeds. As long as the incubation time became greater, the estimated size of the mineralizable N pool was larger and the estimated mineralization rate became smaller. These results suggested that the exponential models did not conform to the actual N mineralization process and that the assumption of the existence of discrete size pools of mineralizable N is a faulty concept.
in N,, and k estimates were generated by the assumption that the mineralization rate is a constant.
INTRODUCTlON Stanford and Smith (1972) proposed a simple exponcntial equation to dcscribc the soil N mineralization process. This equation is of the form: N,,, = N
MATERIALSAND Cenlrul Jinile fiiferences
(I -c-“)
where N,, is the accumulated N mincralizcd at time r, N is the mineralizable N pool at time I and k is the mineralization rate constant. From this model the potentially mincralizablc N of soils (N,) may be cstimatcd. N, is assumed to be a pool of rcadilymincralizablc N which is mincralizcd at a rate proportional to the size of the pool. The proccdurc proposed by Stanford and Smith (1972) involves the incubation of soil samples to determine N,,,; N, and k were estimated by an iterative method. Later, the procedure has been modified to improve the estimates accuracy (Smith er al., 1980; Sierra and Barberis. 1983). Some authors (Molina er al., 1980; Richter er al.. 1982; Deans ef al.. 1986) observed that the simple exponential equation did not fit satisfactorily the experimental data, they proposed a double exponential equation in order to improve the agreement with actual observations. This model assumes the existence of two pools of mineralizable N with different mineralization rate constant. It appeared from these studies that the double exponential model had a better fit with measured mineralized N. Cabrera and Kissel (1988) have shown that as the incubation time incrcascd. the estimated N0 increased and the estimated k decreased, therefore the N,, and k estimates were unstable; a similar conclusion was obtained by other authors by using both models (Nordmeyer and Richter, 1985; Bonde and Rosswall. 1987). The aim of this paper was to discuss the deficiencies of the exponential models and to analyze if the errors *Present
Saint
address: Station d’Agronomie Paul. BP 91. 84143 Montfavet
INRA. Cedex,
Domaine France. IIS1
METHODS
appro.rimdon
The simple cxponcntial
model
N,,, = N*(l -c-“)
(1)
is the solution of the first order difkrcntial dN/dt = -k IN
equation (2)
where N is the mineralizable N at time I. k is the mineralization rate constant and N,,, is the accumulated N mineralized at time 1. This model assumes a single mineralizable N pool of discrete size with a single mineralization rate constant. In this paper equation (2) was analyzed using the method proposed by Sierra and Barberis (1983). which is based on the central finite differences approximation to the differential equation. Thus dN/dt may be approximated by AN/At, where AN is the difference of accumulated N mineralized at two consecutive times (Al). So, AN/At = INm(r,) - N,(Gll[r, - (,I
(3)
where N,,,(t,) and N,,,(f3 are the accumulated N mineralized at time I, and t2, respectively. On the other hand, -k + N [equation (2)j may be approximated by -k I N(t,), where N(I,) is the mineralizable N at time t, is the intermediate time between t, and I*. It comes, -k + N(t,) = -k
l[N(t,)
- NJr,)]
(4)
where N(r,) is the initial mineralizable N (= N. or potentially mineralizable N). The N,(tJ was estimated by a parabolic function such as N,,,=artb
(5)
where a and b are fitted empirical constants. This function gave the best fit to the experimental data; the same was obtained by Broadbent (1986).
1152
JORGE Sauu
Combining ]Nnl(r,) -
equations (3) and (4) they become
~m(~:Mh- 41 = -P l N(cJl + [k *~&)I.
A Experimental data L!neaf t,t at t,6 -- L!n=r f!t at tZ3 ---- Lmear fit at t29
(6)
The slope of linear equation (6) is k; N,, [ = N(t,)] may be calculated by dividing the intercept [k * N(t,)] by the slope k. When AN/At = 0 (abscissa’s intercept) then from equation (6) ]k l NW1 =
[k l Nn(~,)l
(7)
and N(r,) = N,(t,) when the straight line intercepts abscissa, therefore N, also may be estimated graphically.
100
200 Ng (I@ JP)
Experimental data
The experimental data presented by Sierra and Barberis (1983) were used. Surface samples (O-O.2 m) of two groups of soils were investigated. The first are Typics Argiudolls (20 soils, loam. organic N 0.13-0.25%. pH 5.6-6.7). the other ones are Typics Hapludolls (14 soils, sandy loam. organic N 0. I2-0.20%. pH 6.0-6.7). The soil incubations were made according to the procedure described by Stanford and Smith (1972). Briefly, log of dried soil (sieved to 2 mm) and IO g of sand wcrc mixed and placed into leaching tubes by triplicate and the initial nitrate were Icachcd. After lcaching procedure the soils were allowed to drain under vacuum and then the water tension was adjusted to 0.33 bar, the samples wcrc then kept at 35°C. Subscqucnt leachings wcrc conducted in a similar way after 2.4, 8. 12. 16, 23. 29 and 36 weeks of incubation and the N content was dctcrmincd. The ammonium and nitrite contents wcrc ncgligiblc.
Fig. 2. Variation of NOand k estimates as a function of the incubation time (soil No. 1 at Fig. 1). The N,, and k estimates were made at 16 (I,,,). 23 (f2,) and 29 (I~) weeks of incubation.
proceeds, the mineralizable N resistance becomes greater and then the mineralization rate becomes smaller. The mineralization rate is not a constant but a variable depending on the mineralizable N resistance. Thus. when the data were fitted by a linear model [equation (6)] as the greater was the incubation time, the more N, was overestimated and k was undcrestimatcd (Fig. 2). this being due to the linear fit of a curvilinear relationship. The two-pool model can be similarly analyzed. This double exponential model can be expressed as (Molina et al.. -1980).
N,,, = N,*(l -e-‘“I)+
N,r(l
-c-~*‘).
(8)
so, dN,/dt = -k, I N,
WFSULTS AND DISCUSSION
Figure I shows the relationship between AN/At and the accumulated mineralized N (N,,,) for some of the soils used; the relationship was not linear as the simple exponential model assumes [equation (6)]. The mineralization rate, represented by the slope of the curves at Fig. I, decreased as N,,, became greater, therefore k is obviously not a constant. The 34 soils have shown the same pattern. These results are in good agreement with the common knowledge that as the N mineralization
A Soil N* 1 Iliapluddl I A Soil N* 13 tliapludolll . Soil N* 17 IArgiudoll) o Soil N’ ZOtArgiudolll
100
by
AN,/At = -k, I N,(r,)
(IO)
dN,/dr = -k2* N2
(I I)
and
was approximated
by ANJAr = -k2r N&)
(12)
where N, and NZ are the two pools of mineralizable N, k, and k, are the mineralization rate constants of
-
AN/At =- k,N, -k2N2
----
ANz/At=ANl/At=-
k2N2 klNl
200 Nm (I@’ @I
Fig.
was approximated
(9)
I. Relationship between AN/AI and N,,, for some of the soils used.
NdtJ
Fig. 3. Double exponential model--central finite differences approximation.
Soil N mineralization estimate
AN/At = - ktN, - k2N2-kgN~-k&N4 - - AN&/At =- k@f, -*- ANvAt=kjNj --- ANz/At=- k2N2 -_-- ANl/At=klNj
1153
paper. it appears that the mineralization rate decreases continuously, then it would not be possible to assume pools of mineralizable N of discrete size as the exponential models propose. From a practical point of view. the number of pools to be included into a model would depend on the purpose of modeling and the accuracy desired. REFERESCES
Bonde T. A. and Rosswall T. (1987) Seasonal variation
Nm(ti) Fig. 4. Exponential able-central
model with four pools of N mineralizfinite differences approximation.
N, and N?, respectively. The result of this analysis is showed in Fig. 3. The double exponential model gives a better fit to the experimental data by considering two mineralizable N pools of different resistance and thus two mineralization rate constants (Molina et al.. 1980); but, as the fit of experimental data is also linear, the mineralizable N (N, and NJ and k (k, and k?) estimates also vary greatly as a function of the incubation time. If scvcral pools of mineralizable N arc included into the model. a group of straight lines with decreasing slope will bc obtained (Fig. 4). the agrecmcnt bctwccn the experimental data and the model will bc greater than with the double cxponcntial model. This agrccmcnt will cnhancc up to include the whole soil N. The results discussed suggest that the simple and the double exponential mod& would be only approximations to the actual mineralization process. Molina cr ul. (1980) and Broadbent (1986) have proposed that the faulty assumption of a single pool of mineralizable N is the reason of the dcficicncies of the simple exponential model. From the present
of potentially mineralizable nitrogen in four cropping systems. Soil Science Society of America Journal 51, 1508-1514. Broadbent F. E. (1986) Empirical modeling of soil nitrogen mineralization. Soil Science 141, 208-213. Cabrera M. L. and Kissel D. E. (1988) Potentially mineralizable nitrogen in disturbed and undisturbed soil samples. Soil Science Society of America Journal 52. 101&1015. Deans J. R.. Molina J. A. E. and Clapp C. E. (1986) Models for predicting potentially mineralizable nitrogen and decomposition rate constants. Soil Science Society of America Journal SO. 323-326. Molina J. A. E., Clnpp C. E. and Larson W. E. (1980) Potentially mineralizable nitrogen in soil: the simple exponential model does not apply for the first I2 weeks of incubation. Soil Science Sorier_v of America Journal44. 442443. Nordmcycr 11. and Richter J. (19X5) Incubation experiments on nitrogen mineralization in locss and sandy soils. Plant and Soil 83. 433-445. Richter J.. Nuskc A., flabcnicht W. and Baucr J. (1982) Optimized N-mineralization parameters of loess soils from incubation expcrimcms. Plunt and Soil 68. 379 ,388. Sierra J. and Barberis L. (1983) Analisis de un modelo de mincralizacion de nirrogcno en suclos dcl oestc de la Provincia de Buenos Aires. Rerisru Fuculfud de Agronnmiu 36. 309 -3 15. Smith J. L., Schnabel R. R.. McNcal B. L. and Campbell G. S. (1980) Potential errors in the lirst-order model for estimating soil nitrogen mincralizalion potenlials. Soil Science Society of America Journul44, 996-1000. Stanford G. and Smith S. J. (1972) Nitrogen mineralization potentials of soils. Soil Science Soriefy o/ Americu Proceedings 36, 465472.
Sod Bid. Biochem. Vol. 22, No. 8. pp. 1151-1153, 1990 Printedin Great Britain.All rights-cd
ANALYSIS OF SOIL NITROGEN MINERALIZATION ESTIMATED BY EXPONENTIAL MODELS
AS
JORGESIERRA* Departamento
Suelos, Facultad de Agronomia
UBA,
(Accepted
Av. San Martin
4453.1417
Buenos Aires. Argentina
5 June 1990)
Summary-The simple and the double exponential models used to describe the soil N mineralization process were analyzed by using a central finite differences approximation. Various investigators have found that these models show deficiencies in estimating the mineralization N pools. This paper investigates the possible causes of such deficiencies. The mineralization rate was observed to decrease continuously as the N mineralization proceeds. As long as the incubation time became greater, the estimated size of the mineralizable N pool was larger and the estimated mineralization rate became smaller. These results suggested that the exponential models did not conform to the actual N mineralization process and that the assumption of the existence of discrete size pools of mineralizable N is a faulty concept.
in N,, and k estimates were generated by the assumption that the mineralization rate is a constant.
INTRODUCTlON Stanford and Smith (1972) proposed a simple exponcntial equation to dcscribc the soil N mineralization process. This equation is of the form: N,,, = N
MATERIALSAND Cenlrul Jinile fiiferences
(I -c-“)
where N,, is the accumulated N mincralizcd at time r, N is the mineralizable N pool at time I and k is the mineralization rate constant. From this model the potentially mincralizablc N of soils (N,) may be cstimatcd. N, is assumed to be a pool of rcadilymincralizablc N which is mincralizcd at a rate proportional to the size of the pool. The proccdurc proposed by Stanford and Smith (1972) involves the incubation of soil samples to determine N,,,; N, and k were estimated by an iterative method. Later, the procedure has been modified to improve the estimates accuracy (Smith er al., 1980; Sierra and Barberis. 1983). Some authors (Molina er al., 1980; Richter er al.. 1982; Deans ef al.. 1986) observed that the simple exponential equation did not fit satisfactorily the experimental data, they proposed a double exponential equation in order to improve the agreement with actual observations. This model assumes the existence of two pools of mineralizable N with different mineralization rate constant. It appeared from these studies that the double exponential model had a better fit with measured mineralized N. Cabrera and Kissel (1988) have shown that as the incubation time incrcascd. the estimated N0 increased and the estimated k decreased, therefore the N,, and k estimates were unstable; a similar conclusion was obtained by other authors by using both models (Nordmeyer and Richter, 1985; Bonde and Rosswall. 1987). The aim of this paper was to discuss the deficiencies of the exponential models and to analyze if the errors *Present
Saint
address: Station d’Agronomie Paul. BP 91. 84143 Montfavet
INRA. Cedex,
Domaine France. IIS1
METHODS
appro.rimdon
The simple cxponcntial
model
N,,, = N*(l -c-“)
(1)
is the solution of the first order difkrcntial dN/dt = -k IN
equation (2)
where N is the mineralizable N at time I. k is the mineralization rate constant and N,,, is the accumulated N mineralized at time 1. This model assumes a single mineralizable N pool of discrete size with a single mineralization rate constant. In this paper equation (2) was analyzed using the method proposed by Sierra and Barberis (1983). which is based on the central finite differences approximation to the differential equation. Thus dN/dt may be approximated by AN/At, where AN is the difference of accumulated N mineralized at two consecutive times (Al). So, AN/At = INm(r,) - N,(Gll[r, - (,I
(3)
where N,,,(t,) and N,,,(f3 are the accumulated N mineralized at time I, and t2, respectively. On the other hand, -k + N [equation (2)j may be approximated by -k I N(t,), where N(I,) is the mineralizable N at time t, is the intermediate time between t, and I*. It comes, -k + N(t,) = -k
l[N(t,)
- NJr,)]
(4)
where N(r,) is the initial mineralizable N (= N. or potentially mineralizable N). The N,(tJ was estimated by a parabolic function such as N,,,=artb
(5)
where a and b are fitted empirical constants. This function gave the best fit to the experimental data; the same was obtained by Broadbent (1986).
1152
JORGE Sauu
Combining ]Nnl(r,) -
equations (3) and (4) they become
~m(~:Mh- 41 = -P l N(cJl + [k *~&)I.
A Experimental data L!neaf t,t at t,6 -- L!n=r f!t at tZ3 ---- Lmear fit at t29
(6)
The slope of linear equation (6) is k; N,, [ = N(t,)] may be calculated by dividing the intercept [k * N(t,)] by the slope k. When AN/At = 0 (abscissa’s intercept) then from equation (6) ]k l NW1 =
[k l Nn(~,)l
(7)
and N(r,) = N,(t,) when the straight line intercepts abscissa, therefore N, also may be estimated graphically.
100
200 Ng (I@ JP)
Experimental data
The experimental data presented by Sierra and Barberis (1983) were used. Surface samples (O-O.2 m) of two groups of soils were investigated. The first are Typics Argiudolls (20 soils, loam. organic N 0.13-0.25%. pH 5.6-6.7). the other ones are Typics Hapludolls (14 soils, sandy loam. organic N 0. I2-0.20%. pH 6.0-6.7). The soil incubations were made according to the procedure described by Stanford and Smith (1972). Briefly, log of dried soil (sieved to 2 mm) and IO g of sand wcrc mixed and placed into leaching tubes by triplicate and the initial nitrate were Icachcd. After lcaching procedure the soils were allowed to drain under vacuum and then the water tension was adjusted to 0.33 bar, the samples wcrc then kept at 35°C. Subscqucnt leachings wcrc conducted in a similar way after 2.4, 8. 12. 16, 23. 29 and 36 weeks of incubation and the N content was dctcrmincd. The ammonium and nitrite contents wcrc ncgligiblc.
Fig. 2. Variation of NOand k estimates as a function of the incubation time (soil No. 1 at Fig. 1). The N,, and k estimates were made at 16 (I,,,). 23 (f2,) and 29 (I~) weeks of incubation.
proceeds, the mineralizable N resistance becomes greater and then the mineralization rate becomes smaller. The mineralization rate is not a constant but a variable depending on the mineralizable N resistance. Thus. when the data were fitted by a linear model [equation (6)] as the greater was the incubation time, the more N, was overestimated and k was undcrestimatcd (Fig. 2). this being due to the linear fit of a curvilinear relationship. The two-pool model can be similarly analyzed. This double exponential model can be expressed as (Molina et al.. -1980).
N,,, = N,*(l -e-‘“I)+
N,r(l
-c-~*‘).
(8)
so, dN,/dt = -k, I N,
WFSULTS AND DISCUSSION
Figure I shows the relationship between AN/At and the accumulated mineralized N (N,,,) for some of the soils used; the relationship was not linear as the simple exponential model assumes [equation (6)]. The mineralization rate, represented by the slope of the curves at Fig. I, decreased as N,,, became greater, therefore k is obviously not a constant. The 34 soils have shown the same pattern. These results are in good agreement with the common knowledge that as the N mineralization
A Soil N* 1 Iliapluddl I A Soil N* 13 tliapludolll . Soil N* 17 IArgiudoll) o Soil N’ ZOtArgiudolll
100
by
AN,/At = -k, I N,(r,)
(IO)
dN,/dr = -k2* N2
(I I)
and
was approximated
by ANJAr = -k2r N&)
(12)
where N, and NZ are the two pools of mineralizable N, k, and k, are the mineralization rate constants of
-
AN/At =- k,N, -k2N2
----
ANz/At=ANl/At=-
k2N2 klNl
200 Nm (I@’ @I
Fig.
was approximated
(9)
I. Relationship between AN/AI and N,,, for some of the soils used.
NdtJ
Fig. 3. Double exponential model--central finite differences approximation.
Soil N mineralization estimate
AN/At = - ktN, - k2N2-kgN~-k&N4 - - AN&/At =- k@f, -*- ANvAt=kjNj --- ANz/At=- k2N2 -_-- ANl/At=klNj
1153
paper. it appears that the mineralization rate decreases continuously, then it would not be possible to assume pools of mineralizable N of discrete size as the exponential models propose. From a practical point of view. the number of pools to be included into a model would depend on the purpose of modeling and the accuracy desired. REFERESCES
Bonde T. A. and Rosswall T. (1987) Seasonal variation
Nm(ti) Fig. 4. Exponential able-central
model with four pools of N mineralizfinite differences approximation.
N, and N?, respectively. The result of this analysis is showed in Fig. 3. The double exponential model gives a better fit to the experimental data by considering two mineralizable N pools of different resistance and thus two mineralization rate constants (Molina et al.. 1980); but, as the fit of experimental data is also linear, the mineralizable N (N, and NJ and k (k, and k?) estimates also vary greatly as a function of the incubation time. If scvcral pools of mineralizable N arc included into the model. a group of straight lines with decreasing slope will bc obtained (Fig. 4). the agrecmcnt bctwccn the experimental data and the model will bc greater than with the double cxponcntial model. This agrccmcnt will cnhancc up to include the whole soil N. The results discussed suggest that the simple and the double exponential mod& would be only approximations to the actual mineralization process. Molina cr ul. (1980) and Broadbent (1986) have proposed that the faulty assumption of a single pool of mineralizable N is the reason of the dcficicncies of the simple exponential model. From the present
of potentially mineralizable nitrogen in four cropping systems. Soil Science Society of America Journal 51, 1508-1514. Broadbent F. E. (1986) Empirical modeling of soil nitrogen mineralization. Soil Science 141, 208-213. Cabrera M. L. and Kissel D. E. (1988) Potentially mineralizable nitrogen in disturbed and undisturbed soil samples. Soil Science Society of America Journal 52. 101&1015. Deans J. R.. Molina J. A. E. and Clapp C. E. (1986) Models for predicting potentially mineralizable nitrogen and decomposition rate constants. Soil Science Society of America Journal SO. 323-326. Molina J. A. E., Clnpp C. E. and Larson W. E. (1980) Potentially mineralizable nitrogen in soil: the simple exponential model does not apply for the first I2 weeks of incubation. Soil Science Sorier_v of America Journal44. 442443. Nordmcycr 11. and Richter J. (19X5) Incubation experiments on nitrogen mineralization in locss and sandy soils. Plant and Soil 83. 433-445. Richter J.. Nuskc A., flabcnicht W. and Baucr J. (1982) Optimized N-mineralization parameters of loess soils from incubation expcrimcms. Plunt and Soil 68. 379 ,388. Sierra J. and Barberis L. (1983) Analisis de un modelo de mincralizacion de nirrogcno en suclos dcl oestc de la Provincia de Buenos Aires. Rerisru Fuculfud de Agronnmiu 36. 309 -3 15. Smith J. L., Schnabel R. R.. McNcal B. L. and Campbell G. S. (1980) Potential errors in the lirst-order model for estimating soil nitrogen mincralizalion potenlials. Soil Science Society of America Journul44, 996-1000. Stanford G. and Smith S. J. (1972) Nitrogen mineralization potentials of soils. Soil Science Soriefy o/ Americu Proceedings 36, 465472.